But they still would be limited to only what monkeys can actually do with typewriters given enough time or monkeys to do everything a monkey will do with a typewriter.
Infinity only allows anything that can happen to happen no matter how unlikely to happen, but it doesn’t allow something that has 0% likelihood to happen like a monkey turning into a cup to happen. If there are any 0% probability events necessary for the task then it wouldn’t happen regardless of the number of monkeys or given time.
But they still would be limited to only what monkeys can actually do with typewriters given enough time or monkeys to do everything a monkey will do with a typewriter.
Not arguing this at all, I think a lot of people get hung up on this though because they don’t actually know what’s “possible or impossible” in our universe, which may not in fact have a good answer. All that aside, it’s just a thought experiment to reveal the inherent problems with working with infinities, because the number of “possible” things that can happen are quite radical.
Yeah I think we’re on the same page there, I was just pointing out a limitation of the thought experiment that draws attention to the fact that infinity only allows what’s improbable possible and doesn’t make the impossible possible. But yeah it doesn’t undermine the idea that introducing infinities gives unintuitive results.
I agree, and I think it’s an absolutely fascinating area to study, because it does touch on some very important questions about our universe. We still don’t know if on the most fundamental levels, if our universe is constrained in some way, or if given enough time everything can change including those constants. I think about this a lot, but there are a surprising number of people who can’t grasp the ideas and problems, so apologies if I came on strong, I just want to make sure we’re all talking about the same things.
Yeah I think the recentness of formalizing infinities into math with Newton’s and Leibnez’s calculus (infinite series, limits approaching infinity) in the 1600s and Cantor’s sets (cardinality of infinite sets) in the late 1800s speaks to the difficulty of even conceptualizing the problems they introduce and the rigor needed to handle them
But they still would be limited to only what monkeys can actually do with typewriters given enough time or monkeys to do everything a monkey will do with a typewriter.
Infinity only allows anything that can happen to happen no matter how unlikely to happen, but it doesn’t allow something that has 0% likelihood to happen like a monkey turning into a cup to happen. If there are any 0% probability events necessary for the task then it wouldn’t happen regardless of the number of monkeys or given time.
Not arguing this at all, I think a lot of people get hung up on this though because they don’t actually know what’s “possible or impossible” in our universe, which may not in fact have a good answer. All that aside, it’s just a thought experiment to reveal the inherent problems with working with infinities, because the number of “possible” things that can happen are quite radical.
Yeah I think we’re on the same page there, I was just pointing out a limitation of the thought experiment that draws attention to the fact that infinity only allows what’s improbable possible and doesn’t make the impossible possible. But yeah it doesn’t undermine the idea that introducing infinities gives unintuitive results.
I agree, and I think it’s an absolutely fascinating area to study, because it does touch on some very important questions about our universe. We still don’t know if on the most fundamental levels, if our universe is constrained in some way, or if given enough time everything can change including those constants. I think about this a lot, but there are a surprising number of people who can’t grasp the ideas and problems, so apologies if I came on strong, I just want to make sure we’re all talking about the same things.
Yeah I think the recentness of formalizing infinities into math with Newton’s and Leibnez’s calculus (infinite series, limits approaching infinity) in the 1600s and Cantor’s sets (cardinality of infinite sets) in the late 1800s speaks to the difficulty of even conceptualizing the problems they introduce and the rigor needed to handle them